William Friedkin's 1973 film The Exorcist set the bar impossibly high for subsequent horror directors. Often parodied, never bettered, Linda Blair's head-turning projectile vomiting – not to mention her character's enterprising use of a crucifix for a sex toy – have led others to the painful realisation that they are only ever going to be trapped in slavish imitation of this ground-breaking hardcore horror classic.

You may be forgiven, then, for hearing demonic cackling at the news that BBC1 has made a prime-time drama series in which the central character is a Vatican exorcist. Our man with the rosary is to be played by Martin Shaw – the former Professionals beefcake turned crusading barrister Judge John Deed. But even more eye-catching is that for Shaw, Apparitions is not just another acting gig – the six-part series is his brainchild. Furthermore, it's one he hopes will inject some "positivity" into our lives. Scary stuff indeed.

"I had the idea and thank God the BBC went along with it," he says, without irony. "It came out of what is now 45 years in the business and my sense of what ought to be done and what was missing. I thought there was too much law, too many cops and too much medicine, so let's do something else'.

A priest, though, and one without a romantic backstory. This isn't going to be The Thorn Birds. "No it isn't. We definitely didn't want that. But it has to be dramatic and at the same time I wanted to see if there was a way of putting across a message of positivity. It coalesced into the idea of a priest because that would give a reason for positivity, for faith, for goodness...."

All of which might suggest that Shaw has quietly turned into the slightly crackers lovechild of Mary Whitehouse and Cliff Richard, but he seemed perfectly sane when I met him. It's just that he feels that most drama these days is a "bit of a downer".

"Apparitions evolved out of wanting to do something different and something positive," he says. "Then it was just a question of handing it over to Joe Ahearne, who is a national treasure as far as I am concerned, and it is unbelievable what he has done."

That could be the masterstroke. Ahearne, who combines credits as both writer and director on Apparitions, cut his teeth on This Life, BBC2's fondly remembered (until an ill-advised belated return) Nineties saga of young urban professionals. His first solo credit, Ultraviolet, became something of a cult item with its tale of modern vampires, and more recently Ahearne has found a natural home in the creative hot house of Doctor Who.

"The original idea for Apparitions was of a priest who is working to promote candidates for sainthood," says Ahearne. "I discovered in research that the issues in exorcism and possession were much more exciting than the usual horror approach to them. I loved the idea that extreme sanctity and extreme evil were interwoven."

The opening episode begins strikingly with the exorcism of Mother Teresa on her deathbed in Calcutta. "It's true. Mother Teresa was exorcised before she died in 1997, and I don't think that's as unusual as it sounds," says Shaw. "Because the Catholic church would say – and it makes sense to me – that the more holy somebody is the more likely they are to come under attack from the Devil."

Shaw plays Father Jacob, whose day job is promoting candidates for sainthood, but who's also a dab hand at driving out demons. The actor says exorcisms are more common than most people believe: "While we were filming, someone brought in a newspaper cutting reporting that Pope Benedict was asking for there to be an exorcist in every parish; clearly he feels it's necessary."

Research was scrupulous, he says. "All the ecclesiastical processes are shown. We had a Roman Catholic priest with us at all times and I said to the priest, 'If at any time you're unhappy with anything, just come and tell me.' But we never had that remark at all."

I bet they didn't. For all its explicit, post-watershed storytelling, Apparitions could well go out instead of Songs of Praise. Not only is it gripping drama, it's terrific Christian propaganda. What may be more shocking for some viewers than the demonic business with vomit, bleeding eyeballs and the Tourette's-style obscenities, is how seriously the drama takes religion. Never mind upsetting Catholics, Apparitions could well end up offending atheists.

A "devout atheist" himself, Ahearne says "the inspiration for the series comes from the Catholic Church – its theology and beliefs. Because many of those beliefs are out of place in a secular society like Britain, this creates great conflict which is the engine for great drama.

"I have a new shelf of literature at home relating to miracle investigation, histories of the saints, exorcism and the nature of evil, but I also have books from the current wave of atheist writers denouncing religion as poison." And in Apparitions it's the demons who get to paraphrase Richard Dawkins.

Martin Shaw admits to a more ecumenical sort of belief than his character. "I'm not a Christian, but I believe in God and I believe in spirituality." And exorcism isn't a completely exotic idea, he says, in a society full of new-age remedies. "I think it depends on what names you apply to something. I mean, I don't know whether you've been to an alternative therapist or a cranial osteopath and reflexologists and so on. Sometimes, particularly with the more subtle forms of osteopathy, they're not even touching you. Strip the osteopath naked and put a bone through his nose and you'd say he was a witch doctor. "The stuff the Catholic church does is labelled exorcism, but I've had a Buddhist priest bless my house and it was just different words."

Dabbling in the occult can spook a man, but Shaw says nothing untoward occurred to him during the shoot. And Ahearne says that although he bought a crucifix in Rome, which he still wears, "Some actors had unnerving stories to tell during the shoot, but not me. My unfaith remains unshaken. I need big miracles to make me believe."

What is clear is that Apparitions has all the potential to be laughable, sub-Dennis Wheatley-style hokum. What makes it seriously entertaining hokum (or realist drama if you believe in demonic possession) is the combination of Shaw's screen presence – imagine Robson Green in the role and shudder – and Ahearne's smart and modern script. And to enjoy the show it's no more necessary to believe in God than it's necessary to believe in aliens to watch The X-Files or vampires to enjoy Buffy (or Ahearne's Ultraviolet).

What is equally impressive is that the series eschews a knowing irony; it's played dead straight. There's an almost subliminal one-shot homage to Max von Sydow in The Exorcist, but that is all. Is Shaw lining up a return series? "That is our hope, and the BBC have optioned one. But whether it goes forward is in the hands of the viewing public, the hierarchy at the BBC, and God." The hierarchy at the BBC probably wouldn't disagree with that pecking order.

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